Entry Matthews:2009:OSM from toplas.bib
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BibTeX entry
@Article{Matthews:2009:OSM,
author = "Jacob Matthews and Robert Bruce Findler",
title = "Operational semantics for multi-language programs",
journal = j-TOPLAS,
volume = "31",
number = "3",
pages = "12:1--12:44",
month = apr,
year = "2009",
CODEN = "ATPSDT",
DOI = "http://doi.acm.org/10.1145/1498926.1498930",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Thu Apr 16 14:08:54 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/;
http://www.math.utah.edu/pub/tex/bib/toplas.bib",
abstract = "Interoperability is big business, a fact to which
.NET, the JVM, and COM can attest. Language designers
are well aware of this, and they are designing
programming languages that reflect it --- for instance,
SML.NET, F\#, Mondrian, and Scala all treat
interoperability as a central design feature. Still,
current multi-language research tends not to focus on
the semantics of these features, but only on how to
implement them efficiently. In this article, we attempt
to rectify that by giving a technique for specifying
the operational semantics of a multi-language system as
a composition of the models of its constituent
languages. Our technique abstracts away the low-level
details of interoperability like garbage collection and
representation coherence, and lets us focus on semantic
properties like type-safety, equivalence, and
termination behavior. In doing so it allows us to adapt
standard theoretical techniques such as
subject-reduction, logical relations, and operational
equivalence for use on multi-language systems.
Generally speaking, our proofs of properties in a
multi-language context are mutually referential
versions of their single language counterparts.\par
We demonstrate our technique with a series of
strategies for embedding a Scheme-like language into an
ML-like language. We start by connecting very simple
languages with a very simple strategy, and work our way
up to languages that interact in sophisticated ways and
have sophisticated features such as polymorphism and
effects. Along the way, we prove relevant results such
as type-soundness and termination for each system we
present using adaptations of standard
techniques.\par
Beyond giving simple expressive models, our studies
have uncovered several interesting facts about
interoperability. For example, higher-order function
contracts naturally emerge as the glue to ensure that
interoperating languages respect each other's type
systems. Our models also predict that the embedding
strategy where foreign values are opaque is as
expressive as the embedding strategy where foreign
values are translated to corresponding values in the
other language, and we were able to experimentally
verify this behavior using PLT Scheme's foreign
function interface.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Programming Languages and
Systems",
keywords = "interoperability; Operational semantics",
}
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14(4)574,
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14(1)107,
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4(4)650,
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4(2)179,
13(1)150,
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21(2)240
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14(2)147,
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16(5)1431,
17(1)47,
17(1)63,
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21(5)914,
28(4)715,
29(5)24,
32(3)7,
33(1)5,
33(5)16
- implement,
4(1)83,
4(2)125,
4(2)149,
14(3)417,
16(1)151,
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16(3)872,
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21(3)569,
21(5)895,
22(1)129,
22(2)224,
22(3)471,
28(5)942,
30(6)30,
32(4)12
- instance,
13(2)237,
14(3)339,
15(1)1,
16(3)607,
16(5)1431,
16(5)1613,
16(6)1842,
17(2)264,
18(2)175,
20(4)869,
21(3)627,
22(5)816,
22(5)861,
22(6)1002,
28(5)795,
33(3)11
- interact,
20(3)483,
22(6)1037,
28(2)290,
30(3)17
- interesting,
4(4)585,
14(4)490,
15(1)36,
15(4)735,
16(3)1051,
17(2)293,
17(5)777,
19(3)413,
19(3)444,
21(1)90,
27(6)1147,
31(2)8,
32(5)18,
33(1)3
- interface,
7(2)214,
8(3)273,
8(4)419,
8(4)524,
9(1)1,
9(2)164,
9(3)297,
10(2)215,
10(4)627,
10(4)633,
11(1)1,
12(2)143,
12(4)501,
12(4)566,
12(4)670,
14(2)201,
14(3)339,
14(4)471,
15(5)876,
16(1)151,
16(2)259,
16(3)370,
16(4)1361,
16(5)1572,
18(1)1,
18(1)30,
19(1)153,
21(4)813,
21(6)1077,
28(2)207,
28(3)517,
30(4)18,
30(6)33,
32(2)6,
33(4)12,
33(4)14
- interoperability,
31(1)5
- JVM,
22(3)471,
22(4)638,
27(6)1097,
28(1)1,
28(4)619,
29(1)4,
30(4)21
- let,
14(3)299,
16(4)1248,
32(3)9,
32(4)12
- level, low-,
16(5)1613,
19(1)153,
19(4)568,
20(6)1131,
21(3)527,
30(4)18,
32(3)7,
32(4)12
- like,
4(4)711,
6(4)546,
7(4)501,
10(2)248,
15(5)876,
17(2)264,
18(6)752,
19(1)87,
19(3)492,
20(4)869,
20(5)1067,
21(4)790,
21(5)914,
21(5)1028,
29(5)29,
31(6)20,
32(5)19,
33(6)20
- logical,
4(1)83,
4(2)125,
8(1)50,
8(4)524,
8(4)577,
15(4)706,
16(3)607,
16(3)727,
16(3)775,
16(3)872,
19(5)751,
20(4)768,
20(5)1067,
29(2)8,
31(2)7,
31(3)11,
31(4)16,
31(5)19,
32(3)7,
32(6)24,
33(5)16,
33(5)17,
33(6)19
- low-level,
16(5)1613,
19(1)153,
19(4)568,
20(6)1131,
21(3)527,
30(4)18,
32(3)7,
32(4)12
- mutually,
32(1)1
- naturally,
13(2)211,
14(4)589,
28(3)429,
31(2)7
- only,
4(2)149,
4(3)382,
4(4)668,
4(4)687,
6(4)527,
7(1)62,
8(4)491,
9(2)235,
9(3)319,
9(4)473,
10(2)204,
13(1)1,
14(1)28,
14(3)299,
14(3)339,
14(3)417,
14(4)574,
15(1)73,
15(4)632,
15(5)745,
16(3)428,
16(3)649,
16(3)687,
16(3)939,
16(3)986,
16(3)1010,
16(5)1648,
17(1)63,
17(2)197,
17(3)431,
18(1)30,
18(1)73,
18(4)355,
18(4)401,
18(4)424,
18(6)711,
18(6)752,
19(3)525,
19(6)1031,
19(6)1085,
20(1)51,
20(3)483,
20(3)546,
20(4)869,
20(6)1251,
20(6)1265,
21(3)502,
21(3)677,
21(6)1077,
22(1)1,
22(1)162,
22(2)224,
22(2)296,
22(3)471,
22(3)540,
22(4)638,
22(4)701,
27(6)1097,
27(6)1270,
28(1)106,
28(2)290,
28(2)331,
28(3)476,
28(5)795,
28(5)908,
29(5)29,
31(1)3,
31(1)4,
31(3)10,
31(4)13,
31(4)15,
31(6)21,
32(1)3,
32(3)9,
32(4)15,
32(6)22,
33(1)4
- operational,
4(2)283,
4(2)295,
4(4)668,
9(4)473,
10(1)118,
11(4)598,
13(1)99,
13(2)237,
13(2)269,
14(4)589,
15(2)211,
15(4)681,
16(3)649,
16(4)1081,
16(4)1215,
16(4)1279,
17(1)47,
18(6)711,
18(6)730,
19(1)48,
19(2)334,
19(5)804,
20(4)768,
20(5)1014,
21(1)90,
21(3)527,
22(2)340,
22(4)701,
22(6)1037,
27(6)1147,
28(2)256,
28(2)290,
28(4)619,
30(5)26,
31(2)6,
31(2)8,
32(5)19
- order, higher-,
14(2)147,
16(5)1411,
16(5)1431,
17(1)47,
17(1)63,
17(4)576,
17(5)704,
18(2)175,
18(4)401,
19(2)334,
19(5)751,
20(1)166,
20(4)845,
21(5)914,
28(4)715,
29(5)24,
32(3)7,
33(1)5,
33(5)16
- polymorphism,
12(1)135,
13(2)237,
13(3)342,
15(2)253,
16(5)1411,
18(5)519,
18(6)711,
19(1)153,
21(1)11,
21(1)90,
21(3)502,
22(1)1,
22(2)340,
28(3)429,
28(5)795,
30(4)18,
32(1)2,
32(3)7
- predict,
16(3)607,
18(4)355,
19(1)188,
20(4)869,
21(4)703,
31(6)20
- prove,
14(2)147,
15(4)575,
15(4)632,
15(4)659,
15(5)771,
16(3)924,
16(3)1051,
16(4)1081,
16(4)1248,
16(5)1411,
16(5)1613,
17(1)47,
17(1)157,
17(2)264,
17(4)576,
18(3)235,
18(3)254,
18(5)519,
18(6)730,
19(3)413,
19(5)804,
19(6)899,
20(4)707,
20(4)724,
20(5)1067,
20(6)1111,
20(6)1171,
21(1)90,
21(2)189,
21(2)240,
21(3)569,
21(3)677,
21(4)790,
21(5)914,
21(6)1196,
22(1)87,
22(2)296,
22(5)773,
22(6)1002,
27(6)1270,
28(2)290,
28(5)795,
28(5)942,
29(6)35,
30(4)24,
31(2)8,
31(5)19,
32(3)7,
32(3)8,
33(4)12,
34(1)2
- rectify,
18(5)528,
28(1)175
- reduction, subject-,
17(1)47
- referential,
17(1)180
- reflect,
14(2)173,
14(3)339,
18(6)649,
19(4)617,
22(3)540,
32(4)14,
32(6)24,
34(1)5
- relation,
2(4)580,
4(3)362,
4(4)615,
8(4)577,
14(3)417,
15(4)575,
15(5)876,
16(2)259,
16(3)607,
16(3)843,
16(3)924,
16(4)1114,
16(5)1449,
16(5)1467,
16(6)1811,
16(6)1842,
17(2)366,
17(3)431,
18(4)401,
19(3)462,
20(1)208,
20(2)302,
20(4)707,
20(4)768,
20(5)1067,
21(3)677,
27(6)1270,
28(4)747,
29(5)29,
30(4)19,
31(2)7,
31(5)19,
32(1)2,
32(2)5,
32(3)7,
32(6)24,
33(4)14
- relevant,
9(3)319,
16(3)387,
17(3)487,
28(3)389
- representation,
1(1)27,
2(2)137,
3(1)111,
3(2)126,
4(3)496,
4(4)527,
7(1)1,
7(1)62,
7(2)270,
7(4)560,
9(2)257,
9(3)297,
9(3)319,
9(4)618,
10(1)118,
10(4)555,
11(1)67,
11(1)115,
11(3)418,
12(1)61,
13(4)626,
14(2)127,
14(2)173,
14(4)574,
14(4)589,
15(5)745,
15(5)876,
16(3)775,
16(6)1842,
17(1)85,
17(2)181,
17(5)777,
19(1)7,
19(3)427,
19(3)462,
19(3)492,
19(5)639,
20(1)1,
20(4)845,
20(5)980,
21(4)703,
21(4)747,
22(1)129,
27(6)1344,
30(6)32,
31(6)21,
32(6)23,
34(1)3
- research,
4(1)1,
8(4)577,
10(2)248,
14(2)147,
15(1)36,
16(1)35,
16(3)328,
17(2)233,
17(3)431,
20(2)274,
20(6)1223,
22(3)506,
27(6)1147,
28(3)476,
30(6)32,
31(5)19
- respect,
5(3)318,
7(1)159,
8(4)524,
8(4)577,
9(2)164,
13(1)99,
13(2)269,
14(2)265,
15(5)876,
16(4)1081,
16(4)1319,
16(4)1361,
16(5)1411,
17(1)47,
17(1)157,
17(2)366,
17(3)487,
17(3)535,
20(3)546,
20(4)724,
22(2)224,
28(2)256,
28(4)619,
28(4)696,
29(1)2,
30(5)25,
32(3)8
- safety, type-,
28(3)429
- scheme,
4(1)37,
4(4)585,
7(4)501,
8(1)109,
10(2)204,
13(3)372,
14(2)147,
14(3)339,
14(4)574,
14(4)589,
16(3)775,
17(4)635,
17(5)704,
18(4)477,
18(6)752,
19(1)87,
20(1)116,
20(1)166,
20(4)768,
20(4)845,
20(6)1195,
21(2)370,
22(1)129,
22(5)861,
27(6)1216,
28(4)715,
28(5)795,
30(5)25,
30(5)28,
30(5)29,
31(1)5,
32(4)13,
34(1)3,
34(1)5
- series,
13(1)52,
18(1)1,
30(3)17
- several,
4(3)362,
4(4)585,
9(2)277,
11(4)633,
13(1)150,
13(2)181,
14(1)54,
14(4)521,
15(1)36,
15(4)632,
15(5)771,
16(3)305,
16(3)428,
16(3)524,
16(3)843,
16(3)924,
16(3)954,
16(3)986,
16(3)1051,
16(4)1114,
16(4)1248,
16(5)1411,
16(6)1661,
17(1)85,
17(1)123,
17(2)181,
17(2)197,
17(2)394,
18(1)1,
18(1)16,
18(4)424,
18(5)528,
19(3)444,
19(3)492,
19(5)639,
19(6)899,
19(6)1031,
20(3)483,
20(4)724,
20(5)917,
20(6)1131,
20(6)1195,
21(1)11,
21(2)175,
21(3)677,
21(6)1137,
21(6)1251,
22(3)540,
22(4)583,
22(4)638,
22(6)1002,
27(6)1147,
28(1)70,
28(4)747,
29(1)3,
29(2)13,
30(1)4,
30(4)19,
30(4)23,
31(1)2,
31(2)7,
31(3)9,
31(4)14,
32(3)9,
32(4)11,
32(5)17,
32(6)21,
33(1)2,
33(4)12,
34(1)2,
34(1)3,
34(1)6
- simple,
4(1)113,
4(2)149,
4(3)455,
4(4)601,
4(4)687,
5(2)127,
6(4)546,
6(4)632,
7(4)637,
10(2)313,
11(1)1,
13(1)124,
13(2)237,
13(2)269,
14(2)147,
15(5)771,
16(3)577,
16(3)607,
16(3)649,
16(3)798,
16(3)872,
16(4)1215,
16(4)1319,
16(4)1361,
16(5)1472,
16(5)1613,
16(6)1737,
17(1)16,
17(1)85,
17(2)233,
17(3)461,
17(4)635,
18(1)1,
18(2)175,
18(4)424,
18(4)454,
18(5)564,
18(6)649,
18(6)730,
19(5)685,
19(5)804,
20(1)51,
20(1)116,
20(3)546,
20(3)679,
20(4)869,
20(5)980,
20(5)1067,
20(6)1297,
21(1)46,
21(2)240,
21(3)502,
21(3)677,
21(4)813,
21(5)895,
22(2)187,
22(2)265,
22(3)490,
22(4)701,
22(6)1002,
30(1)4,
30(4)23,
30(5)26,
30(6)31,
31(3)10,
31(4)16,
31(5)18,
31(5)19,
32(1)2,
32(1)3,
32(2)4,
32(3)9,
32(4)11,
32(4)12,
33(1)3,
34(1)3
- single,
4(1)44,
4(2)179,
4(3)382,
8(4)419,
9(3)319,
11(4)491,
13(1)150,
13(4)451,
14(1)1,
14(1)107,
14(2)201,
14(4)574,
15(4)632,
16(3)524,
16(3)986,
16(4)1114,
16(4)1117,
16(5)1648,
16(6)1661,
16(6)1768,
16(6)1842,
17(1)63,
17(1)85,
17(3)535,
17(5)777,
18(3)235,
18(5)528,
20(1)51,
20(3)483,
20(4)869,
21(1)46,
21(3)627,
21(5)895,
21(5)948,
21(5)977,
21(5)1028,
22(4)583,
22(5)773,
22(5)816,
22(6)1002,
28(1)70,
28(2)331,
30(4)21,
30(4)23,
30(5)28,
30(6)32,
30(6)33,
31(6)20,
32(3)9,
34(1)5
- sophisticated,
16(1)35,
16(6)1768,
21(2)189,
32(1)3,
32(5)16,
34(1)3
- standard,
4(1)113,
4(2)239,
9(4)491,
10(2)189,
13(1)124,
13(2)269,
14(2)127,
14(2)265,
15(2)211,
16(3)649,
16(4)1117,
16(4)1248,
16(5)1411,
16(6)1699,
17(2)366,
17(5)777,
18(1)73,
18(2)109,
18(2)139,
18(3)254,
18(3)268,
18(3)325,
18(4)355,
18(5)519,
19(3)413,
19(4)586,
20(2)259,
20(2)302,
20(3)483,
20(4)707,
20(4)724,
20(6)1171,
20(6)1265,
21(3)430,
21(4)790,
21(4)813,
21(5)914,
21(6)1196,
22(1)129,
22(4)638,
22(4)701,
28(2)207,
28(5)908,
29(5)29,
30(4)21,
30(5)25,
30(5)28,
31(5)18,
34(1)2,
34(1)3,
34(1)4
- start,
4(3)496,
14(4)471,
20(3)483
- still,
4(1)44,
4(4)650,
16(3)328,
16(3)1024,
17(1)47,
20(2)274,
20(6)1171,
27(6)1147,
28(1)106,
29(2)13,
33(3)10,
34(1)5
- strategy,
2(1)18,
6(4)487,
6(4)603,
7(1)62,
7(3)490,
8(3)406,
10(4)555,
11(3)388,
13(3)315,
14(1)1,
14(2)147,
14(2)265,
15(4)659,
16(3)1010,
16(4)1215,
16(6)1768,
18(1)30,
18(4)424,
18(4)454,
18(5)528,
18(5)615,
18(6)730,
20(1)208,
20(2)344,
20(4)707,
21(2)240,
21(3)430,
22(4)638,
28(3)389,
28(3)517,
28(5)908,
30(4)23,
31(2)7,
31(4)14,
33(1)2,
33(1)3,
33(3)11
- subject-reduction,
17(1)47
- techniques.,
16(4)1156
- termination,
2(1)42,
2(3)463,
3(1)112,
4(1)37,
4(3)455,
5(3)356,
6(3)370,
8(3)388,
15(1)1,
15(5)771,
16(2)259,
16(4)1081,
20(1)208,
20(3)586,
20(6)1171,
21(6)1137,
22(1)45,
22(4)583,
27(6)1147,
28(2)256,
28(4)747,
29(1)5,
29(2)10,
29(3)15,
30(3)16,
31(3)10,
32(3)8,
32(5)16,
33(2)7
- theoretical,
9(4)491,
14(1)54,
14(2)147,
16(1)35,
16(4)1117,
20(4)707,
20(4)768,
20(6)1195,
21(2)370,
21(4)813,
21(5)914,
22(5)861
- translated,
4(1)21,
14(3)299,
18(6)752
- treat,
31(1)4
- type-safety,
28(3)429
- value,
4(1)44,
4(2)226,
4(3)323,
4(4)527,
6(4)527,
7(3)426,
8(4)419,
8(4)577,
9(3)367,
9(3)408,
10(2)189,
13(2)181,
13(2)237,
13(2)269,
14(4)471,
15(5)876,
16(1)35,
16(3)387,
16(3)428,
16(4)1279,
16(5)1411,
16(5)1449,
16(6)1675,
17(1)63,
17(2)181,
17(2)394,
17(4)561,
18(3)254,
18(6)730,
20(2)302,
20(3)635,
20(4)724,
20(6)1111,
21(1)138,
21(2)286,
22(2)340,
22(5)932,
22(6)1037,
28(3)389,
28(3)429,
30(4)18,
31(3)10,
32(1)2,
32(3)7,
32(4)11,
32(4)15,
32(5)17,
32(6)23,
32(6)24,
33(5)16
- verify,
16(1)35,
16(3)872,
16(5)1512,
17(2)197,
19(5)726,
20(6)1223,
21(2)370,
30(4)20,
30(6)30,
31(1)1,
31(1)5,
32(3)7,
32(4)14,
32(5)16,
32(5)18,
33(1)4,
34(1)2
- version,
4(2)125,
4(2)295,
4(3)362,
4(4)650,
6(2)215,
7(4)501,
8(2)244,
8(3)273,
9(2)277,
10(3)470,
10(4)627,
10(4)633,
11(3)345,
14(4)589,
15(2)211,
15(4)735,
16(3)428,
16(3)775,
16(5)1543,
16(6)1768,
16(6)1875,
17(4)672,
18(4)424,
18(6)711,
19(4)557,
19(6)899,
20(5)980,
20(6)1297,
21(2)286,
22(1)129,
22(5)773,
22(5)932,
22(6)1037,
27(6)1049,
30(1)4,
30(3)17,
31(3)9,
33(3)9
- very,
3(2)126,
4(3)402,
4(4)650,
5(2)164,
9(2)198,
9(2)235,
13(1)99,
14(1)107,
16(3)872,
16(5)1431,
16(6)1768,
17(1)63,
17(2)233,
17(2)394,
17(3)461,
17(4)635,
17(5)740,
18(3)268,
19(3)525,
19(4)617,
20(6)1265,
21(2)286,
21(4)813,
22(2)296,
22(4)583,
22(6)1002,
30(5)28
- way,
4(2)226,
4(4)687,
7(2)183,
7(3)404,
8(4)419,
9(2)257,
9(4)491,
10(2)189,
10(2)248,
15(4)659,
15(5)876,
16(2)205,
16(2)259,
16(4)1114,
16(6)1675,
16(6)1768,
16(6)1811,
17(2)181,
17(2)264,
17(2)331,
17(2)366,
18(1)1,
18(1)73,
18(4)477,
19(1)7,
19(3)444,
19(3)492,
19(5)804,
19(6)916,
20(1)208,
20(2)259,
20(2)344,
20(4)869,
20(6)1171,
21(1)46,
21(3)527,
21(3)569,
22(2)187,
22(3)506,
22(4)701,
22(6)1002,
22(6)1037,
28(3)389,
28(3)476,
28(3)517,
28(4)747,
30(4)19,
30(4)21,
30(4)23,
31(4)16,
32(1)3,
32(2)5,
32(5)19,
32(6)24,
33(3)10
- well,
4(2)125,
4(2)258,
4(4)687,
7(1)159,
9(2)125,
12(4)643,
13(1)52,
13(1)99,
14(2)265,
15(1)1,
15(4)659,
16(3)305,
16(4)1081,
16(4)1097,
16(4)1319,
16(5)1399,
16(6)1875,
17(1)28,
17(1)85,
17(2)197,
17(5)740,
17(5)777,
19(3)413,
19(4)568,
19(6)992,
19(6)1053,
20(1)208,
20(2)344,
20(3)483,
20(3)546,
20(4)707,
21(1)1,
21(3)430,
21(4)703,
21(4)747,
21(5)948,
22(2)187,
28(1)175,
30(4)19,
30(4)20,
30(5)25,
31(3)10,
33(1)5,
33(5)16,
34(1)3,
34(1)4
- were,
16(3)305,
17(2)197,
17(3)487,
18(1)1,
18(4)424,
20(3)483,
20(6)1131,
23(2)105,
27(6)1344,
28(5)848,
29(1)3,
30(4)20,
31(6)22,
32(1)3,
33(3)9,
33(4)13
- where,
4(3)382,
4(4)527,
7(1)62,
8(4)419,
9(2)164,
9(3)367,
10(2)189,
11(4)633,
13(2)237,
14(2)201,
15(4)659,
16(2)259,
16(3)387,
16(3)775,
16(3)954,
16(4)1117,
16(4)1319,
16(6)1699,
16(6)1842,
16(6)1875,
17(1)123,
17(1)157,
17(2)264,
17(3)487,
17(4)600,
18(1)30,
19(3)462,
20(3)679,
20(5)1067,
20(6)1223,
20(6)1251,
20(6)1297,
21(1)11,
21(3)527,
21(4)703,
21(4)813,
21(5)895,
21(5)1028,
21(6)1077,
21(6)1196,
22(1)129,
22(2)378,
22(4)701,
22(5)816,
27(6)1147,
27(6)1270,
27(6)1344,
28(2)256,
30(1)4,
30(4)23,
31(3)9,
31(3)11,
31(4)14,
31(4)15,
31(4)16,
31(6)20,
32(1)2,
32(2)6,
32(4)13,
33(5)15,
33(6)21,
34(1)3
- work,
4(1)1,
4(2)283,
4(4)678,
4(4)687,
4(4)711,
6(2)159,
6(4)527,
8(4)419,
9(2)257,
9(3)408,
10(2)248,
13(1)124,
14(3)299,
14(4)574,
15(1)36,
16(1)35,
16(3)607,
16(4)1097,
16(4)1117,
16(4)1319,
16(5)1543,
16(6)1675,
17(1)1,
17(2)181,
17(2)233,
17(4)561,
17(5)691,
18(2)109,
18(4)454,
18(5)615,
18(6)730,
19(1)1,
19(4)617,
19(5)639,
19(6)916,
20(1)1,
20(1)208,
20(4)768,
20(4)845,
20(6)1195,
20(6)1223,
21(1)46,
21(2)240,
21(3)527,
21(4)703,
21(5)1028,
21(6)1251,
22(2)265,
22(4)701,
22(6)1002,
27(6)1097,
28(1)1,
28(1)70,
28(1)175,
28(4)619,
28(5)795,
28(5)848,
28(5)908,
29(1)2,
30(3)17,
30(4)22,
30(5)25,
31(3)9,
31(5)18,
31(5)19,
32(1)3,
32(3)9,
32(4)13,
32(6)23,
33(3)9,
33(3)10,
33(4)13,
33(4)14,
33(6)20,
34(1)2,
34(1)4,
34(1)5